How many moles of iron is equivalent to 4.45 x 10^22 atoms of iron

Explanation:

We are asked to convert a number of iron atoms to moles of iron.  

We will use Avogadro's Number for this, which is 6.022 × 10²³. This is the number of particles (atoms, molecules, formula units, etc.) in 1 mole of a substance. For this problem, the particles are atoms of iron. There are 6.022 ×10²³ atoms of iron in 1 mole of iron.  

We will also use dimensional analysis to solve this problem. To do this, we use ratios. Set up a ratio using the underlined information.

Since we are converting 4.45 × 10²² atoms of iron to moles, we multiply the ratio by that value.

Flip the ratio. The value is the same, but it allows us to cancel the units of atoms of iron.

Condense into 1 fraction.

The original measurement of atoms ( 4.45 × 10²²) has 3 significaint figures, so our answer must have the same. For the number we calculated, that is the ten-thousandths place. The 9 to the right of this place (0.07389571571) tells us to round the 8 up to a 9.

There are approximately 0.0739 moles of iron in 4.45 × 10²² atoms of iron.  

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